Integrating Computing with Geometry into an Upper-Level Computer Science Curriculum

计算机科学(31)由于世界是围绕几何对象建立的，计算机科学和工程中的许多领域都专注于表示、处理和建模几何对象，这一点也就不足为奇了。这些熟悉的领域包括计算机图形学、计算机辅助设计、3D视觉、可视化、机器人学、NC加工、分子建模、地形建模和地理信息系统。然而，典型的计算机科学课程对几何计算的讨论很少，甚至没有讨论。该项目解决了在培训未来计算机专业人员方面的这一不足，特别是在越来越多的应用程序需要具有几何和建模技能的训练有素的程序员的时候。这个项目是之前一个非常成功的概念验证项目的延伸，即本科计算机科学课程中的几何计算。基于网络的教科书和软件工具DesignMentor在全世界范围内开发和使用，并受到高度评价。该项目建立在前一个项目的经验教训以及来自世界各地的教师和用户的经验的基础上。这个项目的主要目标是设计和开发一套全面的、初级的和灵活的课程材料，用于教学几何计算的主题，可以在一门专门的课程中使用，也可以在几门课程(例如，几何计算、计算机图形学、计算机辅助设计、几何建模和可视化)中使用。第二个目标是开发工具，使学生能够以直观的、非数学的、边做边学的方式对概念、几何算法和技能进行实验和可视化。通过一套组织良好的当代课程材料和教学工具，我们希望学生能够熟悉几何世界中最先进的计算技术，获得基本知识和技能，知道如何在不同的应用和环境中处理几何问题，并做好充分准备，自信地处理几何应用程序及其软件开发。此外，该项目还可能提高学生的保留率，特别是那些在传统课程中可能表现不佳的几何思维学生，在计算机科学方面。另一方面，这个项目也可能帮助可视化和几何能力较弱的学生提高技能。最重要的是，这个项目通过培养计算机科学家、数学家和工程师，为需要扎实的几何计算基础的职业培养人才，从而影响未来。

Computer Science (31)Since this world is built around geometric objects, we should not be surprised that many areas in computer science and engineering focus on representing, processing, and modeling geometric objects. These familiar areas include computer graphics, computer-aided design, 3D vision, visualization, robotics, NC machining, molecular modeling, terrain modeling and GIS. However, a typical computer science curriculum has a little or even no discussion about computing with geometry. This project addresses this deficiency in the training of future computer professionals, especially at a time that more and more applications require highly trained programmers with geometric and modeling skills. This project is an extension of a previous very successful proof-of-concept project, Geometric Computing in the Undergraduate Computer Science Curricula. A web-based textbook and a software tool DesignMentor were developed and used worldwide and are highly regarded. The project builds on the lessons learned in this previous project and on the experiences of instructors and users from all over the world. The primary goal of this project is to design and develop a set of comprehensive, elementary, and flexible course materials for teaching topics in computing with geometry that can be used in a dedicated course or across several courses (e.g., computing with geometry, computer graphics, computer-aided design, geometric modeling, and visualization). A secondary goal is to develop tools with which students can experiment and visualize the concepts, geometric algorithms, and skills in an intuitive, non-mathematical, and learning-by-doing way. With a set of well-organized contemporary course materials and pedagogical tools, we expect that students will be familiar with the state-of-the-art of computing in the geometric world, acquire basic knowledge and skills, know how to handle geometric problems in different applications and environments, and be well-prepared to approach geometric applications and their software development with confidence. Moreover, this project may also improve the retention rate of students, especially those geometric-minded students who may not perform well in traditional courses, in computer science. On the other hand, this project may also help students who are weak in visualization and geometry to improve their skills. Most importantly, this project impacts the future by preparing computer scientists, mathematicians, and engineers for professions that need a solid foundation in computing with geometry.